This inventions relates to method and apparatus for carrying out mathematical computations, such as with computers and calculating devices. More particularly, this invention relates to carrying out mathematical computations with terms that include a scalar part and a unit part such as length, mass, time, etc.
Mathematical computations often involve physical terms that have units such as a length, a temperature, a voltage, etc. In the process of carrying out a computation with multiple terms, units may be converted to a dimensionally consistent unit, such as inches to feet, or cancelled if the same unit appears in both the numerator and denominator of the final result. Conventional calculating devices such as calculators and computers are not equipped to manage physical units in mathematical computations. The manipulation of physical units is typically limited to providing conversion factors for converting a scalar associated with one type of unit to a scalar associated with another type of unit, such as converting 18 inches to 1.5 feet.
Mathematical computations involving physical units are thus split into two steps. First, one must write out the computations manually, usually with pencil and paper, and then resolve the units using conversion factors. Then a calculating device is used to perform the numerical calculations and the conversions. This two-step method is not only slow but is also prone to error. In attempting to resolve the units one can mistakenly combine dimensionally inconsistent units, such as inches and gallons, and not catch the error.